Extraneural electrodes are the only class of peripheral nerve interface to be chronically implanted in humans to address functional deficits due to neurological impairment. Chronically implanted cuff electrodes have been used to stimulate motor nerves that innervate the lower- and upper-limb musculature to correct excessive foot drop in individuals following stroke and to produce functional movements such as hand grasping and standing in individuals with spinal cord injury (Hoffer & Kallesoe, 2001). Stimulation of ventral sacral roots in humans using cuff electrodes have been implanted in thousands of paralyzed people to restore the volitional control of bladder and bowel function as well as sexual function (Brindley, 1977). Microchannel electrode arrays developed recently have shown promise as a tool to incorporate sensory feedback of bladder fullness into a closed-loop bladder control system (Chew et al., 2013).
The early success of cuff electrodes as long-term interfaces for recording neural activity in peripheral nerves (Brindley, 1977; Hoffer & Kallesoe, 2001; R. B. Stein et al., 1975; R. B. Stein, Nichols, Jhamandas, Davis, & Charles, 1977) motivated the development of early mathematical models to better understand the relationship between action potentials, channel configuration, and the signals one could expect to record (Marks & Loeb, 1976; R. Stein & Pearson, 1971). These models were developed under two critical assumptions, namely that 1) radial currents, perpendicular to the long axis of the channel, are zero, and 2) the extracellular potentials at both ends of the channel are always zero. Modeling studies use a recording electrode fixed at mid-channel to explore the dependency of extracellular potentials on other parameters, such as action potential shape and conduction velocity, proximity of nodes of Ranvier to the recording electrode, and cuff length and diameter (Marks & Loeb, 1976; R. Stein & Pearson, 1971; Johannes Jan Struijk, 1997).